Abstract
We present a relatively new and very efficient method to find approximate analytical solutions for a very general class of nonlinear fractional Volterra and Fredholm integro-differential equations. The test problems included and the comparison with previous results by other methods clearly illustrate the simplicity and accuracy of the method.
Highlights
The two mathematicians Vito Volterra and Erik Ivar Fredholm, through their works published in the early 1900s, laid the foundations of the modern theory of integro-differential equations
To find approximate numerical solutions to nonlinear fractional Volterra and Fredholm integro-differential equations, Block-pulse Functions Methods used by Ali et al in 2019 ([25]) and by Saadatmandi and Akhlaghi in 2020 ([26]) to solve fractional Fredholm–Volterra integrodifferential equations, The Müntz–Legendre Polynomials Method used by Sabermahani and Ordokhani in
We presented the Polynomial Least Squares Method as a straightforward, efficient and accurate method to find approximate analytical solutions for a very general class of fractional nonlinear Volterra–Fredholm integro-differential equations
Summary
The two mathematicians Vito Volterra and Erik Ivar Fredholm, through their works published in the early 1900s, laid the foundations of the modern theory of integro-differential equations. Among the methods used to compute approximate analytical and numerical solutions for fractional Volterra and Fredholm integro-differential equations we mention:. To find approximate numerical solutions to nonlinear fractional Volterra and Fredholm integro-differential equations, Block-pulse Functions Methods used by Ali et al in 2019 ([25]) and by Saadatmandi and Akhlaghi in 2020 ([26]) to solve fractional Fredholm–Volterra integrodifferential equations, The Müntz–Legendre Polynomials Method used by Sabermahani and Ordokhani in. Together with initial conditions (2) (if present) admits a solution This class of equations is a very general one since it includes both Fredholm and Volterra-type equations, linear and nonlinear, and both integro-differential and integral equations. Least Squares Method (denoted from this point forward as PLSM), in Section 3 we present the results of an extensive testing process involving most of the usual test problems included in similar studies, and in Section 4 we present the conclusions of the study
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